Morphometric Analysis

A Brief History and Data Types

Dean Adams, Iowa State University

07 October, 2019

Motivation

“The study of form may be descriptive merely, or it may become analytical. We begin by describing the shape of an object in simple words of common speech: we end by defining it in the precise language of mathematics; and the one method tends to follow the other in strict scientific order and historical continuity.”

D’Arcy Thompson. (1915). Trans. Roy. Soc. Edinburgh

Morphometrics

Why Study Shape?

Why Study Shape?

To properly study shape we require a definition of it

Form and Shape

Early Uses of Morphology

Transformation Grids in Art: Durer (1528)

Transformation Grids in Biology

Early versions were qualitative. This week we learn the thin-plate spline which enables accurate shape transformations

The Biometric Tradition

Development of Statistics

Multivariate Morphometrics

Multivariate Morphometrics

Geometric Morphometrics

Measuring Shapes

Measuring Shapes

Measuring Shapes

Morphometric Data

Homology in Morphometrics

Data Types: Linear Measurements

Linear Measurements: Considerations

Advantages

Disadvantages

Linear Measures: Same Values Different Shapes

Linear Measures: Same Values Different Shapes

Something is missing! The relative positions of the distances on the structure

The Truss

The Morphometric Revolution

This advance was aided by the simultaneous development of mathematical shape theory

Data Types: Landmark Coordinates

Types of Landmarks

Landmarks: Considerations

Advantages

Disadvantages

These issues are alleviated through Geometric Morphometric methods and its extensions to other data types, see further on

Data Types: Curves

Curves: Considerations

Advantages

Disadvantages

But see next! – The Procrustes paradigm allows the combination of points, curves and surfaces

Semilandmarks

Semilandmarks: Considerations

Advantages

The Procrustes Paradigm

General Morphometric Protocol

Special Considerations: Missing Data

Special Considerations: Symmetry

Dean’s View of Quantitative Biology